Two classes of non-weight modules over the twisted Heisenberg-Virasoro algebra

Abstract

In the present paper, we construct two classes of non-weight modules $\Omega (\lambda ,\alpha ,\beta )\otimes \mathrm{Ind}(M)$ and $\mathcal{M}(V,\Omega (\lambda ,\alpha ,\beta ))$ over the twisted Heisenberg-Virasoro algebra, which are both associated with the modules $\Omega (\lambda ,\alpha ,\beta )$. We present the necessary and sufficient conditions under which modules in these two classes are irreducible and isomorphic, and also show that the irreducible modules in these two classes are new. Finally, we construct non-weight modules $\mathrm{Ind}_{\underline y,λ}(\C_{RS})$ and $\mathrm{Ind}_{\underline z,λ}(\C_{PQ})$ over the twisted Heisenberg-Virasoro algebra and then apply the established results to give irreducible conditions for $\mathrm{Ind}_{\underline y,λ}(\C_{RS})$ and $\mathrm{Ind}_{\underline z,λ}(\C_{PQ})$.

References in corpus (7)

• $\mathcal{U}(\mathfrak{h})$-free modules and coherent families
• Modules over the Heisenberg-Virasoro and $W(2,2)$ algebras
• Whittaker Modules for the twisted Heisenberg-Virasoro Algebra
• Irreducible Virasoro modules from tensor products
• Tensor product weight modules over the Virasoro algebra
• Harish-Chandra Modules Over the Twisted Heisenberg-Virasoro Algebra
• Subsingular vectors in Verma modules, and tensor product modules over the twisted Heisenberg-Virasoro algebra and W(2,2) algebra

Cited by in corpus (1)

• Derivations, 2-local derivations, biderivations and automorphisms of generalized Loop Heisenberg-Virasoro algebras